So insurance costs may be a factor, but its doubtful that its a large factor in healthcare costs, they largest factor is by far the public vs private system.
I experienced US healthcare when I went to visit a doctor in the US for a simple (obvious) ear infection. I was charged $600 USD for a five minute consult because the doctor wanted to milk as much $$$ from me as he could, giving me lots of unrelated/pointless blood tests (which were pointless because I was flying out the next day and wouldn't get the results).
In Australia it would have been a $65 fee paid by the government, and $10 for the antibiotics, around 1/10th of the US costs.
The problem in the US is that doctors and hospitals are incentivised to give patients unnecessary tests and medication, because it inflates their bills, and they make more profit.
I've noticed the same thing happening in Australia with private vets & vet hospitals because they are less regulated. They try and talk you into a lot of unnecessary procedures, test, and drugs because they make more profit, and the industry is not where near as well regulated as healthcare.
At least with a vet you can usually shop around, when you are sick often you cannot.